basics

Question 1

number sequences

give an example

Answer 1

numbers arranged according to a rule

even by 2:2 4 6 8

Question 2

even numbers

Answer 2

numbers that divide evenly

Question 3

odd numbers

Answer 3

numbers that divide evenly with a remainder of one

Question 4

square numbers

Answer 4

multiply a number by itself gives square numbers

Question 5

composite numbers

Answer 5

numbers that can be arranged in at least two rows and two columns

Question 6

prime numbers

list the first seven prime numbers

Answer 6

numbers that cannot be boxed

3 5 7 11 13 17 19

Question 7

exponents

Answer 7

also called powers, multiplies a number by itself a given number (the exponent) of times

2⁴=16

Question 8

the numberline

Answer 8

used to represent a sequence of numbers

Question 9

zero

Answer 9

referred to as the empty set

Question 10

multiples

Answer 10

the results of multiplication

Question 11

1. fractions
2. what property of numbers do fractions allow for?
3. what is the name of this property?

Answer 11

1. the numbers in between other whole numbers
2. in between fractions exists more fractions
3. this property is called the density of numbers

Question 12

sets

Answer 12

groups of numbers

Question 13

4 important sets

Answer 13

1. counting numbers
2. intergers
3. rational numbers
4. real numbers

Question 14

the counting numbers set

Answer 14

a.k.a natural numbers because they arrise naturally from observing the world

closed under multiplication and division

Question 15

what does it mean when a set is closed under an operation?

Answer 15

if you perform the stated operation on a number from the set with another number from the same set, you will always get another number from that same set

Question 16

intergers

Answer 16

1. encompasses zero, negative numbers, natural numbers
2. closed under multiplication, addition and subtraction

Question 17

rational numbers

Answer 17

1. include intergers and fractions
2. closed under multiplication, division, addition and subtraction

Question 18

real numbers

Answer 18

1. composed of rational and irrational numbers

Question 19

irrational numbers

Answer 19

1. neither whole nor fractions
2. can only be written as non repeating decimals that do not fall into any pattern of number repetitions
3. PI is an irrational number

Question 20

digit

Answer 20

single numerical symbols from zero to nine

Question 21

numbers

Answer 21

a single digit or a string of digits

Question 22

place value

Answer 22

each digit in a number is 10 times greater than the number to its right

Question 23

what number acts as a place holder?

when is a place holder significant?

Answer 23

1. zero
2. zero’s appearing to the right of a number add value and are significant

Question 24

what is a leading zero?

Answer 24

zero’s to the left of a number which can be dropped

Question 25

and

Answer 25

in math represents a decimal point

Question 26

what is the special symbol for approximations?

Answer 26

≈

Question 27

addition

Answer 27

1. result: sum 2. first and second: addends

Question 28

multiplication

Answer 28

1. result: product 2. factors are multiplied a. first: multiplicand; second: multiplyer

Question 29

division

Answer 29

1. result: quotient 2. first: dividend; second: divisor

Question 30

subtraction

Answer 30

1. result: difference 2. first: subtrahend second: minvend

Question 31

inverse give examples

Answer 31

operations that undo what another operation does 1. addition and subtraction are inverse 2. multiplication and division are inverse

Question 32

commutative operations

Answer 32

allow for switching number order around without changing the results multiplication and addition are commutative

Question 33

associative operations

Answer 33

allows for grouping numbers differently without changing the results addition and multiplication

Question 34

distributive property

Answer 34

allows for splitting large multiplication problems into smaller ones

Question 35

adding and subtracting negatives

Answer 35

1. adding negatives results in a lower negative number - 10+-10=-20 2. subtracting negative numbers: the two negative signs cancel each other out

Question 36

multiplication and division with negative numbers

Answer 36

1. same signed numbers result in positive numbers 2. opposite signs result in negatives

Question 37

unit

Answer 37

1. anything that can be counted a. units must be identical to be added and subtracted b. units can be multiplied and divided by numbers only if the units are objects and not abstacts

Question 38

exponents

Answer 38

shorthand for repeated multiplication of a number 1. base numbers are the numbers being multiplied 2. exponents are the number of times the number is to be multiplied

Question 39

squared numbers

Answer 39

base numbers raised to the 2'nd power or x²

Question 40

roots

Answer 40

the inverse operations of exponents finding the square root of a number is the most common root operation: use of the radical symbolizes a square root operation

Question 41

absolute value

Answer 41

the positve value of any number I-6I=6 shows how many numbers any given number is away from zero

Question 42

equation

Answer 42

is a statement with an equal sign that signifies two things have the same value two basic types: arithmetic and algebraic

Question 43

two properties of equality

Answer 43

1. reflexivity everything is equal to itself 2. symmetry allows switching around the order in which things are equal

Question 44

expression

Answer 44

string of mathematical symbols that can be placed on either side of an equation

Question 45

evaluation

Answer 45

solving act of finding the value of an expression allows taking an expression and turning it into an equation with an equal sign

Question 46

order of operations

Answer 46

evaluate an expression from left to right in this order: 1. parenthesis 2. exponents 3. multiplication and division 4. addition and subtraction